ok, this should work because I've done it a couple of times and it never failed.
boot a vps with the same os and rsync the following directories back as root:
don't just rsync / because you should not mess with the /dev and /proc directories etc.
for example a restore command for your /home directory would be
rsync -avp --progress --delete --numeric-ids /vpsbackup/home/ firstname.lastname@example.org:/home/
(assuming your backup is in /vpsbackup)